Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11763813 | C2 | semidirect |
| 3. C4×C4⋊#595 | C2 | semidirect |
| 4. #11763679 | C2 | semidirect |
| 10. C4×Q8×C17 | C4 | semidirect |
| 11. Q8×Dic17 | C4 | semidirect |
| 13. #10587579 | C4 | semidirect |
| 17. C4×D68 | C4 | semidirect |
| 64. Q8×C17 | C4⋊C4 | semidirect |
| 77. D68 | C4⋊C4 | semidirect |
| 102. C4×C17 | #104 | semidirect |
| 124. C4×Q8 | #595 | semidirect |
| 139. C17 | #1806 | semidirect |
| 177. Q8 | C4⋊#595 | semidirect |
| 222. C4 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763813 | 2 |
| C2×#10587550 | 2 |
| C4×C4⋊#595 | 2 |
| #11763679 | 2 |
| C4×#63256 | 2 |
| #1806 | 17 |